He started his hockey career with Lokomotiv-2 Yaroslavl in the Pervaya Liga and played a season with them.

He then moved to North America to play for the Drummondville Voltigeurs of the Quebec Major Junior Hockey League. During his time in the QMJHL, he led all of the Quebec League blueliners with 62 points in 57 games and won a bunch of trophies which included the Emile Bouchard Trophy as the QMJHL Defenceman of the Year; the Raymond Lagacé Trophy as the Defensive Rookie of the Year; and the Mike Bossy Trophy as the league's best pro prospect.

He was drafted with the 14th overall pick in the 2009 NHL Entry Draft by the Florida Panthers. The Panthers signed Kulikov on September 29, 2009.[1] He has shown high levels of skill and confidence after playing in 68 games with the Florida Panthers.